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Calculus Derivatives
Calculus Derivatives
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Answers
1
Which DOES NOT belong?
slope of the tangent line
integral
derivative
instantaneous rate of change
2
Differentiate implicitly to find dy/dx in terms of
x
and
y: x
ln
y = 10
4
.
dy/dx = 0
dy/dx = 4000y
dy/dx = −lny
dy/dx = −ylny/x
3
Given the position s(t), estimate the instantaneous velocity as
t
gets close to 5 numerically.
13
5
12
0
4
Which is
true
about the function
f
of the graph?
The limit of f as x approaches 1 does not exist.
f is continuous at x = −2.
The limit of f as x approaches 4 from the left is ∞.
f is undefined at x = −2.
5
Find the derivative of y = sin x
2
.
y' = 2xcos x2
y' = 2xsin x2
y' = 2cos x
y' = cos x2
6
Find the value of the derivative at the given point.
0
13
22
−74
7
Find dy/dx:
y
= sec e
x
.
dy/dx = exsec ex
dy/dx = sec extan ex
dy/dx = exsec extan ex
dy/dx = exsec x tan x
8
The function has a non-removable discontinuity at
x
= 0.
False
True
9
An open box is to be made from a rectangle 20x30 units, by cutting squares from each corner. Write the volume function.
V = (30-x)(20-x)
V = (30-2x)(20-2x)
V = x(30-x)(20-x)
V = x(30-2x)(20-2x)
10
Given
d(t)
=18
t
− 4.9
t
2
, the displacement of the football above the ground. At
t
= 3, the football is going down.
True
False
